MULTIPLYING POLYNOMIALS

In this lesson on Multiplying Polynomials, we will learn:

• Multiplying monomials
• Multiplying binomials briefly and
• Multiplying polynomials

• Pre-requisites for understanding this multiplying polynomials lesson:

  • Laws of Exponents
  • What are Polynomials?
  • Math Properties of Arithmetic operations such as
  • Distributive property
  • Commutative property and

  The following rules for multiplying positive and negative numbers:

  Multiplication Rule 1:

  –  × + = –

  Example 1: 

  – a × +b = – ab

  Multiplication Rule 2:

  × –   = +

  Example 2:

  • a × – b  = +ab

  Multiplication Rule 3:

  +  × –  = – ab

  Example 3:

  + a × –  b= – ab

  Multiplication Rule 4:

  +  × +  = +

  Example 4:

  +a  × + b = + ab

  
  Multiplying polynomials is one of the four fundamental operations of algebraic expressions.

  
   The other three fundamental operations on algebraic expressions are:

  • Addition of polynomials
  • Subtraction of polynomials
  • Division of polynomials

  Now, let us learn Multiplying Polynomials by remembering the following multiplication rules (for multiplying polynomials)

  Step 1: Multiply the Numerical Coefficients separately

  Step 2: Multiply the literal coefficients separately and

  Step 3: Multiply the above two products (the numerical coefficients product and the literal coefficients product)

  SOLVED PROBLEM NO.1:

  Multiply the following two monomials:

  3a² and 5a³

  Step 1: Numerical coefficients product = 3 × 5 = 15

  Step 2: literal coefficients product = a² × a³ = a⁵ (from the law of exponents – if bases are same, then add the powers)

  Step 3:

  Now, write the product of the numerical coefficients (15) and literal coefficients (a5), i.e.

  15 × a⁵ = 15a⁵.

  Note:

  15a⁵ stands for the product of 15 and a⁵, just as

  pq means product of p and q i.e. p × q, and

  3a means 3 × a.

  Now, Multiplying a Monomial with a Binomial

  SOLVED PROBLEM NO 2:

  Multiply  the Monomial 3a² with the binomial x + y

  Solution:

  First set up the product as below:

  3a² × (x + y)

  Now, Recall the distributive property a (b + c) which is:  

  a(b + c) = ab + ac

  So, by applying the above distributive property to 3a² × (x + y), we get

  3a²x + 3a²y.

  SOLVED PROBLEM NO 3:

  Perform the following multiplication of polynomials:

  3a² (5a³b + 6ac)

  Solution:

  From the distributive property a (b + c) = ab + ac,

  We get the following two terms:

  3a² × 5a³b + 3a² × 6ac

  Now from exponents rules, add powers of same bases and applying the following steps:

  Step 1: Multiply the Numerical Coefficients separately

  Step 2: Multiply the literal coefficients separately and

  We get:

  3a² × 5a³b = 3×5×a² ×a³ × b   = 15 a⁵×b and

  3a² × 6ac = 3 × 6 × a² × a × c = 18a³c, so finally the product of

  3a² and (5a³b + 6ac) is 15 a⁵×b + 18a³c.       

  MATH SKILLS RELATED TO MULTIPLYING POLYNOMIALS

  • Worksheets on Multiplying polynomials
  
  
  • Worksheets on Multiplying binomials  
  
  
  • Multiplying Fractions
  
  
  • Multiplying Numbers
  
  
  • Multiplying Decimals
  
  
  • Multiplying Exponents
  
  
  • Multiplying Fractions
  
  
  • Multiplying Matrices
  
  
  • Multiplying Mixed Fractions
  
  
  • Multiplying Polynomials
  
  
  • Multiplying Radicals
  
  
  • 6th grade math
  
  
  • 7th grade math
  
  
  • 8th grade math